Problem: Solve for $x$ and $y$ using elimination. ${-5x+2y = -34}$ ${-3x-2y = -46}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-8x = -80$ $\dfrac{-8x}{{-8}} = \dfrac{-80}{{-8}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-5x+2y = -34}\thinspace$ to find $y$ ${-5}{(10)}{ + 2y = -34}$ $-50+2y = -34$ $-50{+50} + 2y = -34{+50}$ $2y = 16$ $\dfrac{2y}{{2}} = \dfrac{16}{{2}}$ ${y = 8}$ You can also plug ${x = 10}$ into $\thinspace {-3x-2y = -46}\thinspace$ and get the same answer for $y$ : ${-3}{(10)}{ - 2y = -46}$ ${y = 8}$